Asymptotics of RNA shapes

Journal of Computational Biology

Volumn 15, Issue 1, 2008, Pages 31-63

  Lorenz, W A ^a   Ponty, Y ^a   Clote, P ^a  

^a BOSTON COLLEGE   (United States)

Author keywords

Enumerative combinatorics; Generating functions; RNA secondary structure; RNA shapes

Indexed keywords

ALGORITHM; ARTICLE; BIOINFORMATICS; MATHEMATICAL COMPUTING; PRIORITY JOURNAL; RNA SEQUENCE; RNA STRUCTURE;

ALGORITHMS; BASE SEQUENCE; COMPUTATIONAL BIOLOGY; NUCLEIC ACID CONFORMATION; RNA;

EID: 39449108593     PISSN: 10665277     EISSN: None     Source Type: Journal    
DOI: 10.1089/cmb.2006.0153     Document Type: Article

References (49)

1. Altschul, S.F., Gish, W., Miller, W., et al. 1990. Basic local alignment search tool. J. Mol. Biol. 215, 403-410.
2. Altschul, S.F., Madden, T.L., Schaffer, A.A., et al. 1997. Gapped BLAST and PSI-BLAST: a new generation of protein database search programs. Nucleic Acids Res. 25, 3389-3402.
3. Banerjee, A.R., Jaeger, J.A., and Turner, D.H. 1993. Thermal unfolding of a group I ribozyme: The low-temperature transition is primarily disruption of tertiary structure. Biochemistry 32, 153-163.
4. Bekaert, M., Bidou, L., Denise, A., et al. 2003. Towards a computational model for -1 eukaryotic frameshifting sites. Bioinformatics 19, 327-335.
5. Bender, E.A. 1974. Asymptotic methods in enumeration. SIAM Rev. 16, 485-515.
6. Bousquet-Melou, M. 1992. Convex polyominoes and algebraic languages. J. Phys. A 25, 1935-1944.
7. Brown, C., Hendrich, B., Rupert, J., et al. 1992. The human XIST gene: analysis of a 17-kb inactive X-specific RNA that contains conserved repeats and is highly localized within the nucleus. Cell 71, 527-542.
8. Canfield, E.R. 1984. Remarks on an asymptotic method in combinatorics. J. Combin. Theor. 37, 348-352.
9. Churchill, R.V. 1960. Complex Variables and Applications. McGraw-Hill, New York.
10. Clote, P. 2006. Combinatorics of saturated secondary structures of RNA. J. Comput. Biol. 13, 1640-1657.
11. Clote, P., and Backofen, R. 2000. Computational Molecular Biology: An Introduction. John Wiley & Sons, New York.
12. Commans, S., and Böck, A. 1999. Selenocysteine inserting tRNAs: an overview. FEMS Microbiol. Rev. 23, 333-351.
13. Denise, A., Roques, O., and Termier, M. 2000. Random generation of words of context-free languages according to the frequencies of letters, 113-125. In: Gardy, D., and Mokkadem, A., eds., Mathematics and Computer Science: Algorithms, Trees, Combinatorics and Probabilities, Trends in Mathematics. Birkhaüser, Berlin.
14. Doudna, J.A., and Cech, T.R. 2002. The chemical repertoire of natural ribozymes. Nature, 418, 222-228.
15. Flajolet, P. 2002. Singular combinatorics. Proc. Int. Congr. Math. 3, 561-571.
16. Flajolet, P., and Odlyzko, A.M. 1990. Singularity analysis of generating functions. SIAM J. Discr. Math. 3, 216-240.
17. Giegerich, R., Voss, B., and Rehmsmeier, M. 2004. Abstract shapes of RNA. Nucleic Acids Res. 32, 4843-4851.
18. Hofacker, I.L., Schuster, P., and Stadler, P.F. 1998. Combinatorics of RNA secondary structures. Discr. Appl. Math. 88, 207-237.
19. Lewis, H.R., and Papadimitriou, C.H. 1997. Elements of the Theory of Computation, 2nd ed. Prentice-Hall, Englewood Cliffs, NJ.
20. Lim, L.P., Glasner, M.E., Yekta, S., et al. 2003. Vertebrate microRNA genes. Science 299, 1540.
21. Markushevich, A.I. 1977. Theory of Functions of a Complex Variable. Chelsea Publishing Company, New York.
22. Mathews, D.H. 2004. Using an RNA secondary structure partition function to determine confidence in base pairs predicted by free energy minimization. RNA 10, 1178-1190.
23. Mathews, D.H., Sabina, J., Zuker, M., et al. 1999. Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure. J. Mol. Biol. 288, 911-940.
24. Mathews, D.H., Turner, D.H., and Zuker, M. 2000. Secondary structure prediction, 11.2.1-11.2.10. In: Beaucage, S., Bergstrom, D.E., Glick, G.D., et al. eds. Current Protocols in Nucleic Acid Chemistry. John Wiley & Sons, New York.
25. McCaskill, J.S. 1990. The equilibrium partition function and base pair binding probabilities for RNA secondary structure. Biopolymers 29, 1105-1119.
26. Meir, A., and Moon, J.W. 1989. On an asymptotic method in enumeration. J. Combin. Theor. 51, 77-89.
27. Moon, S., Byun, Y., Kim, H.-J., et al. 2004. Predicting genes expressed via -1 and +1 frameshifts. Nucleic Acids Res. 32, 4884-4892.
28. Nebel, M. 2003. Combinatorial properties of RNA secondary structures. J. Comput. Biol. 3, 541-574.
29. Nussinov, R., and Jacobson, A.B. 1980. Fast algorithm for predicting the secondary structure of single stranded RNA. Proc. Natl. Acad. Sci. USA 77, 6309-6313.
30. Odlyzko, A.M. 1995. Asymptotic enumeration methods, 1063-1230. In: Graham, R.L., Grötschel, M., and Lovász, L., eds., Handbook of Combinatorics, Volume II. Elsevier Science B.V. and MIT Press, Amsterdam and Cambridge.
31. Penchovsky, R., and Breaker, R.R. 2005. Computational design and experimental validation of oligonucleotide-sensing allosteric ribozymes. Nat. Biotechnol. 23, 1424-1431.
32. Rodland, E.A. 2006. Pseudoknots in RNA secondary structures: representation, enumeration, and prevalence. J. Comput. Biol. 13, 1197-1213.
33. Salvy, B., and Zimmerman, P. 1994. Gfun: a maple package for the manipulation of generating and holonomic functions in one variable. ACM Trans. Math. Software 20, 163-177.
34. Smith, T.F., and Waterman, M.S. 1981. Identification of common molecular subsequences. J. Mol. Biol. 147, 195-197.
35. Steffen, P., Voss, B., Rehmsmeier, M., et al. 2006. RNAshapes: an integrated RNA analysis package based on abstract shapes. Bioinformatics 22, 500-503.
36. Stein, P.R., and Waterman, M.S. 1978. On some new sequences generalizing the Catalan and Motzkin numbers. Discr. Math. 26, 261-272.
37. Tinoco, Jr., I., Borer, P.N., Dengler, B., et al. 1973. Improved estimation of secondary structure in ribonucleic acids. Nat. New Biol. 246, 40-41.
38. Tinoco, Jr., I., and Schmitz, M. 2000. Thermodynamics of formation of secondary structure in nucleic acids, 131-176. In: Cera, E.D., ed., Thermodynamics in Biology. Oxford University Press, New York.
39. Vauchaussade de Chaumont, M., and Viennot, X.G. 1985. Enumeration of RNA's secondary structures by complexity, 360-365. In: Capasso, V., Grosso, E., and Paven-Fontana, S.L., eds., Mathematics in Medicine and Biology, Volume 57. Springer, New York.
40. Vicens, Q., and Cech, T.R. 2006. Atomic level architecture of group I introns revealed. Trends Biochem. Sci. 31, 41-51.
41. Voss, B., Giegerich, R., and Rehmsmeier, M. 2006. Complete probabilistic analysis of RNA shapes. BMC Biol. Feb. 15;4, 5.
42. Walter, P., and Blobel, G. 1982. Signal recognition particle contains a 7S RNA essential for protein translocation across the endoplasmic reticulum. Nature 299, 691-698.
43. Waterman, M.S. 1978. Secondary structure of single stranded nucleic acids. Adv. Math. Suppl. Studies 1, 167-212.
44. Waterman, M.S. 1995. Introduction to Computational Biology - Maps, Sequences and Genomes. Chapman & Hall, New York.
45. Weinger, J.S., Parnell, K.M., Dorner, S., et al. 2004. Substrate-assisted catalysis of peptide bond formation by the ribosome. Nat. Struct. Mol. Biol. 1, 1101-1106.
46. Winkler, W.C., Cohen-Chalamish, S., and Breaker, R.R. 2002. An mRNA structure that controls gene expression by binding FMN. Proc. Natl. Acad. Sci. USA 99, 15908-15913.
47. Xia, Jr., T., SantaLucia, J., Burkard, M.E., et al. 1999. Thermodynamic parameters for an expanded nearest-neighbor model for formation of RNA duplexes with Watson-Crick base pairs. Biochemistry 37, 14719-14735.
48. Zuker, M. 1986. RNA folding prediction: the continued need for interaction between biologists and mathematicians. Lect. Math. Life Sci. 17, 87-124.
49. Zuker, M., and Stiegler, P. 1981. Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information. Nucleic Acids Res. 9, 133-148.